The standard Bayesian framework does not account for the decision maker's errors, such as the conjunction and disjunction fallacies, in updating the belief state upon measuring the uncertain quantities. Moreover, the classical probability theory does not distinguish a mixed state (e.g., being of two minds) from a superposed state (e.g., being of neutral mind). The operator sum representation of completely positive linear maps can address these limitations in a unified manner, and allows for numerical determination of a general belief-state update rule. In particular, examples show that the operator sum approach yields an improvement over the existing quantum model of human inference, and that it can be used to explain the mixing and superposition effects of gossip interactions.
The standard Bayesian framework does not account for the decision maker's errors, such as the conjunction and disjunction fallacies, in updating the belief state upon measuring the uncertain quantities. Moreover, the classical probability theory does not distinguish a mixed state (e.g., being of two minds) from a superposed state (e.g., being of neutral mind). The operator sum representation of completely positive linear maps can address these limitations in a unified manner, and allows for numerical determination of a general belief-state update rule. In particular, examples show that the operator sum approach yields an improvement over the existing quantum model of human inference, and that it can be used to explain the mixing and superposition effects of gossip interactions.
People make logically inconsistent probability judgments.The "Linda" problem is a well-known example, which often elicits a conjunction/disjunction fallacy: probability of constituent event A (B) judged more/less likely than their conjunction/disjunction.The Quantum Judgment model (QJM, Busemeyer et al 2011) explains such errors, which are not explainable within classical probability theory.We propose an alternative axiomatic approach in the framework of quantum probability theory that employs positive operators representing the set of general queries, in constast to QJM which uses projection operators.Like QJM, our model accounts for conjunction/disjunction fallacies, averaging type errors, and unpacking effects, suggesting that it provides a viable model of judgement error.Further differences between our model and QJM are also discussed.
How can we use quantum theory to model other phenomena of interest to researchers in cognition and decision making? Quantum theory is not easy for researchers in cognition and decision making to accept. In fact, quantum mechanics was not easy for physicists to accept either, but it was forced on them by several paradoxical findings that could not be explained using classical physics. We have a similar problem in cognition and decision making – there are numerous paradoxical findings that just seem irrational according to classic probability theory. For example, under some conditions, people judge the probability of event A and B to be greater than the probability of event B , which is called the conjunction fallacy (Tversky & Kahneman, 1983). Also, under the same conditions, they judge the probability of A or B to be less than the probability of event A (Carlson & Yates, 1989), which is called the disjunction fallacy. In this chapter we examine how quantum probability theory explains these and other puzzling results from human probability judgment research. This chapter has two main parts. In the first part, we use a quantum model to derive qualitative predictions for conjunction errors, disjunction errors, and other closely related findings. The first section provides a general set of predictions that do not depend on specific assumptions about the features used to represent events, and the predictions are parameter free. In the second part, we examine the quantitative predictions of the quantum model for a Bayesian inference task, which we use to explain order effects on inference.
There is considerable variety in human inference (e.g., a doctor inferring the presence of a disease, a juror inferring the guilt of a defendant, or someone inferring future weight loss based on diet and exercise). As such, people display a wide range of behaviors when making inference judgments. Sometimes, people's judgments appear Bayesian (i.e., normative), but in other cases, judgments deviate from the normative prescription of classical probability theory. How can we combine both Bayesian and non-Bayesian influences in a principled way? We propose a unified explanation of human inference using quantum probability theory. In our approach, we postulate a hierarchy of mental representations, from 'fully' quantum to 'fully' classical, which could be adopted in different situations. In our hierarchy of models, moving from the lowest level to the highest involves changing assumptions about compatibility (i.e., how joint events are represented). Using results from 3 experiments, we show that our modeling approach explains 5 key phenomena in human inference including order effects, reciprocity (i.e., the inverse fallacy), memorylessness, violations of the Markov condition, and antidiscounting. As far as we are aware, no existing theory or model can explain all 5 phenomena. We also explore transitions in our hierarchy, examining how representations change from more quantum to more classical. We show that classical representations provide a better account of data as individuals gain familiarity with a task. We also show that representations vary between individuals, in a way that relates to a simple measure of cognitive style, the Cognitive Reflection Test. (PsycINFO Database Record
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector spaces defined by features and similarities between vectors to determine probability judgments. On the other hand, quantum probability theory is a generalization of Bayesian probability theory because it is based on a set of (von Neumann) axioms that relax some of the classic (Kolmogorov) axioms. The quantum model is compared and contrasted with other competing explanations for these judgment errors, including the anchoring and adjustment model for probability judgments. In the quantum model, a new fundamental concept in cognition is advanced--the compatibility versus incompatibility of questions and the effect this can have on the sequential order of judgments. We conclude that quantum information-processing principles provide a viable and promising new way to understand human judgment and reasoning.
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning.
This paper investigates how probabilistic graphical models and their quantum extensions can support decision making under uncertainty in robot–human interaction. Using a simple person-following task as a representative example, the study compares a classical Bayesian Network (BN) with two quantum extensions: a quantum-enhanced Bayesian Network (QeBN) and a full Quantum Bayesian Network (QBN). The purpose of this paper is to examine the expressive limitations of classical Bayesian decision models in contexts involving ambiguous sensing and partially conflicting evidence, and to evaluate whether quantum-inspired representations can provide richer and more flexible decision mechanisms while remaining interpretable. In the classical BN, uncertainty in human motion and robot actions is represented through conditional probability distributions, and action selection is performed by marginalizing over hidden variables. This framework supports decision making by combining prior beliefs and sensor-based likelihoods in a principled and computationally efficient manner. However, because inference relies on additive probabilities and conditional independence, alternative explanations contribute only as weighted mixtures, preventing interaction between competing hypotheses. To address this limitation, the paper reviews a QeBN in which classical probabilities are lifted to complex probability amplitudes while the original graph structure is preserved. This extension retains classical marginals but allows phase-dependent interference during marginalization, enabling non-additive belief updates that capture contextual effects such as sensor fusion ambiguity or conflicting cues in human–robot interaction. Building on this, a full QBN formulation is reviewed in which beliefs and conditional relationships are represented directly by quantum states and density operators. Inference is performed through joint state construction, quantum marginalization via partial trace, and measurement-based conditioning, providing a fully quantum-native alternative to classical Bayesian reasoning. Through analytical walk-through examples, the paper clarifies how each framework supports decision making, highlights their conceptual and mathematical differences, and demonstrates how quantum extensions can enhance expressiveness and context sensitivity beyond classical Bayesian models. The results position BN, QeBN, and QBN as complementary tools along a spectrum of decision-making models, offering increasing representational power for robotic systems operating in uncertain and human-centered environments.